All modern rechargeable electronic devices use lithium ion batteries. They come in many many different chemistries and sizes. If you run higher voltage you need less amps. If you need less amps per battery, you can increase the capacity which lowers the draw limit. This is why there are many different chemistries. For example, an 18500 can have a safe draw limit of 50 amps, however its capacity will be limited to 1100mah. Another 18500 with different chemistry could have a 10 amp draw limit, but a capacity of 2000mah.
These chemistries and sizes dictate the capacity, safe draw limit, and safe charge limit.
If you bust open laptop batteries you will find cylinders of these batteries all linked together into a battery pack.
Only a few factories in the world make batteries, most are rebranded and repackaged from just a few roots.
Look into 22mm batteries, 18mm batteries, 26mm batteries, hobby batteries, etc etc etc. The list goes on forever.
Panasonic makes some pretty nice lithium ion batteries IMO. They currently have a 2000mah 18500 that is the bee's knee's as well as a 3400mah 18650.
To complicate this issue further. Some batteries are electronically protected, while others are not and rely on the components of the device to offer protection. Using a protected or unprotected cell is very important and you should always use what the electronic device calls for or it can be damaged. For example, a digital device with its own protection circuit will not get along well with a protected li ion cell.
If you run a lithium ion cell too low, it will "vent" which is a sort of explosion. Devices that use high drain lithium ion cells either require protected cells or have internal protective circuits combined with vents to prevent an explosion of the device in the event the cell fails and vents. It is not a powerful explosion when a cell "vents", more or less similar to fireworks. It can do damage but its not going to cause MAJOR damage.
When my 12 cell lithion ion (3.7v x 12) fails, yes it goes up in flames. When my single cells fail... they don't really do much other than make smoke. I've seen a few 50 amp high drain cells spin on the ground like fireworks and leave a nice scorch mark though.
Safe chemistry lithium ion cells are nothing to be afraid of though, FYI, which is the majority of what we use in our devices.